Solve the equation ?

Solve the equation ?

#(z-1)^3=2-11i#

1 Answer
Manasvini Nittala
Jan 17, 2018

#x^3-iy^3+3ix^2y-3xy^2-3x^2+3y^2-6ixy+3x+3iy##=3-11i#

Explanation:

given #(z-1)^3=2-11i->(1)# expanding it we get
#z^3-1-3z^2+3z=2-11i->(2)#
let us assume #z=x+iy->(3)# put #(3)# in #(2)#
#(x+iy)^3-3(x+iy)^2+3(x+iy)=3-11i#
#x^3-y^3i+3ix^2y-3xy^2-3(x^2-y^2+2ixy)+3(x+iy)# #=3-11i#
#x^3-iy^3+3ix^2y-3xy^2-3x^2+3y^2-6ixy+3x+3iy##=3-11i#

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